Competitive pricing under local network effects

Abstract

This paper will study the pricing problem of two competitive products in a market characterized by local externalities. For this purpose, a stochastic model of sales propagation among consumers is developed. This model utilizes a compartmentalized schema denoted as a Markov Chain where the local network effects impact transition rates. A key aspect of the proposed model is its multilayer structure, where products’ information streams through different layers. The equilibrium conditions and the optimal pricing strategies in a competitive market are examined. The pricing problem is investigated in two settings of homogeneous and heterogeneous (i.e., differential). It is shown that the existence and coexistence of individual products in the equilibrium point depends on an epidemic parameter, called reproduction number, that quantifies the speed by which a product’s sales spread over the network. Moreover, it is found that the correlation between the network’s layers impacts the equilibrium point. Specifically, a negative correlation between the network’s layers allows a wider coexistence region than a positive correlation. Additionally, it is found that a negative correlation between the network’s layers provides more flexibility to firms for their pricing practices and yields a higher profit. Finally, different pricing strategies are characterized with respect to model parameters and the centrality measures of different networks. It is observed that while centrality measures and optimal prices are highly correlated, node centralities alone are not enough to determine optimal prices.